>>11441428I'll try to explain it another way. Look at the pic OP posted. It's a model of the hydrogen atom, specifically modelling the motion of the electron around the nucleus.
You see that scary formula in the top right? That's the wave function of the electron and it completely describes its state. By the phi, we see n, l and m subscripts, they are integers. n tells us the energy state it's in, l is the magnitude angular momentum of the electron, m is the angular momentum measured along an axis. n,l,m aren't actually these values, they parameterize them. For example, angular momentum is hbar*sqrt(l*(l+1)). m ranges from -l to l in integer steps. nlm tell us all the possible states the electron can be in.
The things in parenthesis are position parameters in spherical coordinates. Quantum mechanics is all about finding these wave functions (scattering too). It's usually impossible to find exact answers so we're forced to approximate.
Now to get actual measurable quantities from this wave function, we square it. Now we have a probability distribution of position, it tells us where the particle is most likely to be found, that's what all those pictures are. The numbers in parenthesis are (n, l, m). The bottem left picture is the distribution of electron positions when the electron is in the 4th energy state, 2nd angular momentum state, 2nd component angular momentum state. You can extract other quantities from wave functions like momentum but that's a bit more complicated.
Also notice I haven't mentioned time yet, the wave functions in OP's pic are stationary states which don't depend on time. Time evolution is kinda complicated, not really. Refer to Ehrenfest's theorem if you want a better understanding of the wave function(the wiki article is pretty technical but the introduction stuff is easy enough to follow). Hope this is a bit better.
